Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[71. THEOREMA VI. PROPOSITIO VI.]
[72. THE OREMA VII. PROPOSITIO VII.]
[73. THE OREMA VIII. PROPOSITIO VIII.]
[74. THE OREMA IX. PROPOSITIO IX.]
[75. PROBLEMA I. PROPOSITIO X.]
[76. PROBLEMA II. PROPOSITIO XI.]
[77. PROBLEMA III. PROPOSITIO XII.]
[78. PROBLEMA IIII. PROPOSITIO XIII.]
[79. THEOREMA X. PROPOSITIO XIIII.]
[80. THE OREMA XI. PROPOSITIO XV.]
[81. THE OREMA XII. PROPOSITIO XVI.]
[82. THE OREMA XIII. PROPOSITIO XVII.]
[83. THEOREMA XIIII. PROPOSITIO XVIII.]
[84. THEOREMA XV. PROPOSITIO XIX.]
[85. THE OREMA XVI. PROPOSITIO XX.]
[86. THEOREMA XVII. PROPOSITIO XXI.]
[87. THE OREMA XVIII. PROPOSITIO XXII.]
[88. THEOREMA XIX. PROPOSITIO XXIII.]
[89. PROBLEMA V. PROPOSITIO XXIIII.]
[90. THEOREMA XX. PROPOSITIO XXV.]
[91. THEOREMA XXI. PROPOSITIO XXVI.]
[92. THEOREMA XXII. PROPOSITIO XXVII.]
[93. PROBLEMA VI. PROPOSITIO XX VIII.]
[94. THE OREMA XXIII. PROPOSITIO XXIX.]
[95. THEOREMA XXIIII. PROPOSITIO XXX.]
[96. THEOREMA XXV. PROPOSITIO XXXI.]
[97. FINIS LIBRI DE CENTRO GRAVITATIS SOLIDORVM.]
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DE I _IS_ QVAE VEH. IN AQVA.
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          <pb o="43" file="0097" n="97" rhead="DE I _IS_ QVAE VEH. IN AQVA."/>
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          <head xml:space="preserve">DEMONSTRATIO QVARTAE PARTIS.</head>
          <p>
            <s xml:space="preserve">HABEAT rurſum portio ad humidum in grauitate
              <lb/>
            proportionem quidem maiorem, quàm quadratum f p ad
              <lb/>
            quadratum b d; </s>
            <s xml:space="preserve">minorem uero, quàm quadratum x o ad
              <lb/>
            b d quadratum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam proportionem habet portio ad
              <lb/>
            humidum in grauitate, eandem habeat quadratum, quod
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            fit à linea ψ ad quadratum b d. </s>
            <s xml:space="preserve">erit ψ maior, quàm f p, & </s>
            <s xml:space="preserve">mi
              <lb/>
            nor, quàm x o. </s>
            <s xml:space="preserve">aptetur ergo quæ dam rectalinea i u inter
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            portiones a u q l, a x d interiecta, quæ ſit æqualis ψ, & </s>
            <s xml:space="preserve">ipſi
              <lb/>
            b d æquidiſtans: </s>
            <s xml:space="preserve">occurratq; </s>
            <s xml:space="preserve">reliquæ ſectioni in y. </s>
            <s xml:space="preserve">rurſus
              <lb/>
            u y dupla ipſius y i demonſtrabitur, ſicuti demonſtrata eſt
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            o g ipſius g x dupla. </s>
            <s xml:space="preserve">ducatur autem ab u linea u ο, quæ ſe
              <lb/>
            ctionem a u q l in u contingat: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta a i ad q produca
              <lb/>
            tur. </s>
            <s xml:space="preserve">eodem modo oſtendemus lineam a i ipſi i q æqualem
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            eſſe: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">a q ipſi
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              <anchor type="figure" xlink:label="fig-0097-01a" xlink:href="fig-0097-01"/>
            u ω æquidiſtan-
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            tem. </s>
            <s xml:space="preserve">Demon-
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            ſtrãdum eſt por
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            tionem in humi
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            dum demiſſam,
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            ĩclinatãq; </s>
            <s xml:space="preserve">adeo,
              <lb/>
            ut baſis ipſius
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            non contingat
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            humidũ, ita con
              <lb/>
            ſiſtere, ut baſis
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            in humidũ ma-
              <lb/>
            gis demergatur
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            quam ut in uno
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            puncto eius ſu-
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            perficiem cõtin
              <lb/>
            gat. </s>
            <s xml:space="preserve">Demittatur enim in humidum, ut dictum eſt; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iaceat
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            primo ſic inclinata, ut baſis nullo modo contingat ſuperfi-
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            ciem humidi. </s>
            <s xml:space="preserve">ſecta autem ipſa plano per axem ad humidi</s>
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